Burial at Sea (Bioshock Infinite DLC)

Ok, I just finished the DLC.

 Spoilers regarding the plasmids as vigours, and the end of the DLC

After Burialatsea!Booker accidently caused the death of Anna (by horrible, horrible decapitation, ouch!) he researched an alternate world that he could go to, one where Anna never existed, and he found Rapture. The opening of the tears in the universe was noticed by Suchong, who through the tears saw a world where Fink stole his thunder regarding the Plasmids. because of this, he strived to create Vigours. That is why this Rapture is slightly different to the previous Rapture, because of Comstock messing around with the Tears.

Something weird that I noticed is that in Rapture, there are tears where you can take things from Columbia, like Freight Hooks and Motorized Patriots, but there are also SAMURAI which seem to come from a different place entirely.
There was also a random NPC who mentioned a third city.

I wonder if that is a hint towards the next game? a Japanese/Feudal era Bioshock?

also the Radar Range is the most OP weapon EVER. I love it.

 Regarding Elizabeth

I don't get her motivation, why did she follow Booker all that way, and help him along the way, just to betray him at that moment? Was it all just for revenge?